A small time thief is recruited by a mobster to help with the racketeering. He doesn't like the job, but with the mob on his back, a femme fatale in his bed and a sick friend to care for, he will have to keep all his wits about him.

Norman Puckle, a well-meaning but clumsy grocer's assistant, can't seem to do anything right. After being rejected by Marlene, the love of his life, he attempts suicide, but can't even do that. He is saved from jumping off a cliff at 'Lover's Leap' by a Royal Navy petty officer. He persuades Puckle to join the Royal Navy, where he'll meet 'lots of girls'. Life in the Navy proves not to be as rosy as it's been described, and Puckle fails at every task during basic training. But despite this, he's regarded by the Admiral in charge of a rocket project to be a 'typical average British sailor', and chosen to be the first man to fly into outer space in an experimental rocket.

A madman is on the loose... killing fashion models that appear on the cover of magazines. The police start a manhunt in an attempt to capture the killer.